WALSH COLLEGE QM 20201Statistical Methods for Business NAME

WALSH COLLEGE QM 202-01-Statistical Methods for Business NAME: Btan QUIZ #7-FALL 2015 NAME: INSTRUCTOR: G. Cummings ize needed to provide a margin of error of 2 or less with a .95 The sample size probability when the popula 1. tion standard deviation equals 11 is? (8 points) A random sample of 16 students shows an average age of 25 years anda standard deviation of 2 years. The 98% confidence interval for the true average age of students is? (6 points) 2. 3. In a sample of 500 voters, 400 indicated they favor the incumbent governor. 95% confidence interval of voters not favoring the incumbent is? (6 points) T

Solution

3.

Note that              
              
p^ = point estimate of the population proportion = x / n = (500-400)/500 =   0.2          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.017888544          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.035060902          
lower bound = p^ - z(alpha/2) * sp =   0.164939098          
upper bound = p^ + z(alpha/2) * sp =    0.235060902          
              
Thus, the confidence interval is              
              
(   0.164939098   ,   0.235060902   ) [ANSWER]